Appearing before the largest annual gathering of Jewish community leaders in North America, he called on moderate Arab states to "unite their common interest in preventing Iran from undermining stability in the Middle East."
"If Iran achieves the ability to produce nuclear weapons, as we know it is seeking to do, we will enter a new era of instability unlike any the world has ever seen," Olmert told several thousand members of the United Jewish Communities, an umbrella group for dozens of organizations.
Israel wants peace, he said, but "no longer can the international community afford to hesitate, contemplate or waver in its dealings with this defiant state."
Olmert's appearance came a day after he received reassurances from the Bush administration in Washington that it is not backing down from its view that Iran and its nuclear program are a world threat.
Israel is worried that political fallout from last week's Republican election defeat and rising calls for U.S. engagement with Iran may soften President Bush's resolve against a country whose leader has said the Jewish state should be wiped from the map.
With Olmert at his side following a White House meeting Monday, Bush told reporters that a nuclear-armed Iran not only would threaten Israel but loom as an "incredibly destabilizing" threat to the region and the world.
In his remarks Tuesday, Olmert called Bush "a great friend ... of Israel" but said America must have the support of the international community to "defuse this mortal threat."
It was Olmert's first appearance before the group since an inconclusive war with Hezbollah militants in Lebanon. The audience was silent when he said, "despite all that has been said and written, we stood up to the challenge."
But he was loudly applauded at other points, including when he said Israel will not tolerate "those who challenge Israel's right to exist."
Olmert thanked Jewish organizations for raising hundreds of millions of dollars to assist reconstruction efforts, and said tourism bolstered the nation's spirit in a time of war.
"Our fates are intertwined," he said. "We may be separated by a vast ocean, but our hearts beat together."